{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "width = 6\n",
    "height = 3\n",
    "import matplotlib\n",
    "matplotlib.rcParams['figure.figsize'] = [width, height]\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import hmmlearn\n",
    "\n",
    "from hmmlearn.hmm import GaussianHMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24.1\n",
      "1.14.6\n",
      "0.2.2\n"
     ]
    }
   ],
   "source": [
    "print(pd.__version__)\n",
    "print(np.__version__)\n",
    "print(hmmlearn.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Look at the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "nile = pd.read_csv(\"Nile.csv\", index_col = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>val</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1871</td>\n",
       "      <td>1120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1872</td>\n",
       "      <td>1160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1873</td>\n",
       "      <td>963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1874</td>\n",
       "      <td>1210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1875</td>\n",
       "      <td>1160</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   year   val\n",
       "1  1871  1120\n",
       "2  1872  1160\n",
       "3  1873   963\n",
       "4  1874  1210\n",
       "5  1875  1160"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nile.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc3b30a43c8>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nile.year, nile.val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's take a look at the hmmlearn API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "vals = np.expand_dims(nile.val.values, 1)\n",
    "n_states = 2\n",
    "model = GaussianHMM(n_components=n_states, n_iter=100).fit(vals)\n",
    "hidden_states = model.predict(vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([72, 28])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.bincount(hidden_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc3af7b1748>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hidden_states)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: how can we package this more conveniently?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def fitHMM(vals, n_states):\n",
    "    vals = np.reshape(vals,[len(vals),1])\n",
    "    \n",
    "    # fit Gaussian HMM to Q\n",
    "    model = GaussianHMM(n_components=n_states, n_iter=100).fit(vals)\n",
    "     \n",
    "    # classify each observation as state 0 or 1\n",
    "    hidden_states = model.predict(vals)\n",
    " \n",
    "    # fit HMM parameters\n",
    "    mus = np.squeeze(model.means_)\n",
    "    sigmas = np.squeeze(np.sqrt(model.covars_))\n",
    "    transmat = np.array(model.transmat_)\n",
    "    print(mus)\n",
    "    print(sigmas)\n",
    "    \n",
    "#     # re-order parameters in ascending order of mean of underlying distribution\n",
    "#     idx      = np.argsort(mus)\n",
    "#     mus      = mus[idx]\n",
    "#     sigmas   = sigmas[idx]\n",
    "#     transmat = transmat[idx, :][:, idx]\n",
    "    \n",
    "#     state_dict = {}\n",
    "#     states = [i for i in range(n_states)]\n",
    "#     for i in idx:\n",
    "#         state_dict[i] = states[idx[i]]\n",
    "    \n",
    "#     relabeled_states = [state_dict[h] for h in hidden_states]\n",
    "    relabeled_states = hidden_states\n",
    "    return (relabeled_states, mus, sigmas, transmat, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1097.15261711  850.75596948]\n",
      "[133.74749638 124.44593534]\n"
     ]
    }
   ],
   "source": [
    "hidden_states, mus, sigmas, transmat, model = fitHMM(nile.val.values, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: how might we be able to plot this more sensibly?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_states(ts_vals, states, time_vals):\n",
    "    fig, ax1 = plt.subplots()\n",
    "\n",
    "    color = 'tab:red'\n",
    "    ax1.set_xlabel('Year)')\n",
    "    ax1.set_ylabel('Nile river flow',         color=color)\n",
    "    ax1.plot(time_vals, ts_vals,      color=color)\n",
    "    ax1.tick_params(axis='y',            labelcolor=color)\n",
    "\n",
    "    ax2 = ax1.twinx()  \n",
    "    color = 'tab:blue'\n",
    "    ax2.set_ylabel('Hidden state', color=color)  \n",
    "    ax2.plot(time_vals,states,     color=color)\n",
    "    ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "    fig.tight_layout()  \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_states(nile.val, hidden_states, nile.year)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: can we improve on the analysis above?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cut off the 'special' region"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "        17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]),)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(hidden_states == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1097.27279934  796.01723512  884.82315224]\n",
      "[133.03503832  67.16297958 138.785672  ]\n"
     ]
    }
   ],
   "source": [
    "hidden_states, mus, sigmas, transmat, model = fitHMM(nile.val.values, 3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_states(nile.val, hidden_states, nile.year)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1097.27279934,  796.01723512,  884.82315224])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(precision = 3, suppress = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.964, 0.036, 0.   ],\n",
       "       [0.   , 0.509, 0.491],\n",
       "       [0.   , 0.304, 0.696]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1097.273,  796.017,  884.823])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: generate new synthetic data from the model and then fit it with a fresh HMM model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Easy to sample from an existing HMM model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = np.squeeze(model.sample(1000)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc3af60d7b8>]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Then refit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 805.823 1118.994  875.002]\n",
      "[ 60.68  129.921 143.171]\n"
     ]
    }
   ],
   "source": [
    "hidden_states, mus, sigmas, transmat, model = fitHMM(res, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_states_no_time(ts_vals, states):\n",
    "    fig, ax1 = plt.subplots()\n",
    "\n",
    "    color = 'tab:red'\n",
    "    ax1.set_xlabel('Time)')\n",
    "    ax1.set_ylabel('Value',        color=color)\n",
    "    ax1.plot(ts_vals,              color=color)\n",
    "    ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "    ax2 = ax1.twinx()  \n",
    "    color = 'tab:blue'\n",
    "    ax2.set_ylabel('Hidden state', color=color)  \n",
    "    ax2.plot(states,        color=color)\n",
    "    ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "    fig.tight_layout()  \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_states_no_time(res[1:100], hidden_states[1:100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.323, 0.   , 0.677],\n",
       "       [0.018, 0.981, 0.001],\n",
       "       [0.313, 0.   , 0.687]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
